Fusion welding is used extensively in industries that support the nations energy supply, defense, infrastructure, and standard of living. Safety and reliability of the welded joints are affected by their geometry, composition and structure. This report provides an account of the significant advances made in quantitative understanding of the geometry, composition and various aspects of the weldment structure with financial support from DOE/BES. In particular, this report provides an account of the research conducted under the grant DE-FG02-84ER45158 in this important area and lists all the publications that document the details of the technical accomplishments that resulted from the work.